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Assignment A7: Image Features Solution
1. Use image called MASK in file chars45.mat to study shape analysis using Hu’s moments for the characters:
A,B,C,D,E,F,G,H,I,K,L,M,N,O,R,S,T,U,V,Y
a,c,d,e,f,g,h,i,k,l,m,n,o,p,r,s,t,u,v,y
0,1,2,3,4,5,6,7,8,9
Use a character from the image as a model, (A1, (A2, (A3, (A4, (A5, (A6), for each charac-ter above. Develop the functions listed below and report performance in terms of overall and per character success.
function Mpq = CS4640_central_moment(pts,p,q)
• CS4640_central_moment - compute a central moment
• Mpq = sum sum (xˆp*yˆq)
% x y
• On input:
• pts (nx2 array): row and cols of points
• p (int): exponent for x
• q (int): exponent for y
• On output:
• Mpq (float): Mpq moment
• Call:
• M00 = CS4640_central_moments([1 1; 2 2; 3 3],0,0);
• Author:
• T. Henderson
1
• UU
•
•
function Epq = CS4640_normal_moment(pts,p,q)
• CS4640_normal_moment - compute a central normal moment
% Epq = <pq/M00ˆb where b = 1+(p+q)/2
• On input:
• pts (nx2 array): row and cols of points
• p (int): exponent for x
• q (int): exponent for y
• On output:
• Epq (float): Epq moment
• Call:
• E00 = CS4640_normal_moment([1 1; 2 2; 3 3],0,0);
• Author:
• T. Henderson
• UU
•
%
function H = CS4640_Hu_moments(pts)
• CS4640_Hu_moments - compute Hu’s 6 moments
• On input:
• pts (nx2 array): row and cols of points
• On output:
• H (6x1 vector): Hu moments
• Call:
• H = CS4640_Hu_moments([1 1; 2 2; 3 3]);
• Author:
• T. Henderson
• UU
•
%
function H_models = CS4640_Hu_build(templates)
• CS4640_Hu_models - produce Hu models for image templates
• On input:
• templates (n-element vector struct): template images
• (k).im (MxN binary image): image template
• On output:
• H_models (nx7 array): Hu models
• Call:
• Hm = CS4640_Hu_models(templates);
2
• Author:
• T. Henderson
• UU
•
%
function classes = CS4640_Hu_classify(im,H_models)
• CS4640_Hu_classify - classify characters using Hu models
• On input:
• im (MxN binary image): input image
• H_models (nx7 array): Hu models for n characters
• On output:
• classes (kx2 array): class and distance for each CC
• Call:
• Hm = CS4640_Hu_classify(im,Hm);
• Author:
• T. Henderson
• UU
•
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2. Implement an eigenchars classification approach similar to the eigenfaces method dis-cussed in the text. Develop a template database of 100 images (2 examples of each charac-ter). Build the models and then report performance on overall and per character success on MASK from chars45.mat. Develop the following functions.
function classes = CS4640_Hu_classify(im,H_models)
• CS4640_Hu_classify - classify characters using Hu models
• On input:
• im (MxN binary image): input image
• H_models (nx7 array): Hu models for n characters
• On output:
• classes (kx2 array): class and distance for each CC
• Call:
• Hm = CS4640_Hu_classify(im,Hm);
• Author:
• T. Henderson
• UU
•
%
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function [V,MM,PCA_models] = CS4640_PCA_model(templates)
• CS4640_PCA_model - build PCA model from templates
• On input:
• templates (vector struct): n template images
• (k).im (MxN binary array): template image for character k
• On output:
• V (M*nxM*n array): eigenvectors
• MM (M*nx1 vector): mean vector
• PCA_models (nxk array): weight values for first k eigenvectors
• Call:
• [V,MM,PCA_models] = CS4640_PCA_model(templates);
• Author:
• T. Henderson
• UU
•
%
function c = CS4640_PCA_classify(im,V,MM,PCA_models)
• CS4640_PCA_classify - classify image using PCA models
• On input:
• im (MxN binary array): input image
• V (M*NxM*N array): eigenvectors
• MM (M*Nx1 vector): mean vector
• PCA_models (nxk array): weight values for first k eigenvectors
• On output:
• c (int): class
• Call:
• [V,MM,PCAm] = CS4640_PCA_model(templates);
• Author:
• T. Henderson
• UU
•
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